audio - Extending Goertzel algorithm to 24 kHz, 32 kHz and 48 kHz

I'm learning to implement Goertzel's algorithm to detect DTMF tones from recorded wave files. I got one implemented in python from here. It supports audio sampled at 8 kHz and 16 kHz. I would like to extend it to support audio files sampled at 24 kHz, 32 kHz and 48 kHz.

From the code I got from the link above, I see that the author has set the following precondition parameters/constants:

self.MAX_BINS = 8
if pfreq == 16000:
    self.GOERTZEL_N = 210
    self.SAMPLING_RATE = 16000
else:
    self.GOERTZEL_N = 92
    self.SAMPLING_RATE = 8000

According to this article, before one can do the actual Goertzel, two of the preliminary calculations are:

1. Decide on the sampling rate.


2. Choose the block size, N

So, the author has clearly set block size as 210 for 16k sampled inputs and 92 for 8k sampled inputs. Now, I would like to understand:

1. how the author has arrived at this block size?


2. what would be the block size for 24k, 32k and 48k samples?